What is the probability of winning on a pass and don't pass with full odds (3 4 5x)?

For instance, if you make it past the come out roll, and a 4 is the point, the don't pass bet is twice as likely to win as the pass bet. I'm not referring to the edge here.

What is the probability of winning for both pass and don't pass with full odds without the point specified?

My feeling is that the don't pass is more fun because you win more often (albeit with less money won).

Quote: longtimelancer

My feeling is that the don't pass is more fun because you win more often (albeit with less money won).

I would doubt that because then the Dark Side would not have evolved such a negative reputation amongst the rabble.

You only have to figure out the chance of one winning, and you know the opposite is 100% minus the other.

The 6/8, 5/9, and 4/10 work the same way. The odds for 4 is the same for 10, for example. That should cut out a lot of math involved.

You can figure out the frequency of each number becoming the point. There are 3 ways to hit a 4 out of a possible 24. So the chance the point is 4 is 3/24 (1/8). From there, you know there are 9 ways to "end" the roll-3 ways for a 4 (win) and 6 ways for a 7 (loss), so the chance is 1/3 the pass wins when the point is 4.

If you want to figure the probability "the next point to be established is a 4 and the pass will win", you multiply chance of point being 4 (1/8) by chance of the point being made (1/3), for a total of 1/24...or about 4%.

I'll leave the rest up to you.

Quote: longtimelancer

My feeling is that the don't pass is more fun because you win more often (albeit with less money won).

Both bets pay even money. The don't wins less often and pushes sometimes. Once you make it past the come out roll, of course the don't wins more, but you often don't make it past the come out roll!

Mathematically, DP + max odds is the lowest house edge wager on the table.

It's still a loser, but it's a better bet than any of the others.

It's also a slow way to play. By not placing any other bets, sometimes you just sit there for 15, 20, 30+ rolls waiting for the bet to be resolved.

Quote: longtimelancer

What is the probability of winning for both pass and don't pass with full odds without the point specified?

My feeling is that the don't pass is more fun because you win more often (albeit with less money won).

Yes, sure fun to win more often.
I get for the pass = 67/165 or 40.6061%
(1/12+2/15+25/132)
4&10: 2* 1/8 * 1/3 = 1/12
5&9: 2* 1/6 * 2/5 = 2/15
6&8: 2* 5/24 * 5/11 = 25/132

that makes the don't = 98/165 or 59.3939%

Find a friend that bets the don't pass and does not lay the full odds.
Make only the lay odds bet
should be no problem finding a nice win streak
0% house edge and win win win
Sally

Quote: longtimelancer

For instance, if you make it past the come out roll, and a 4 is the point, the don't pass bet is twice as likely to win as the pass bet. I'm not referring to the edge here.

What is the probability of winning for both pass and don't pass with full odds without the point specified?

I agree with RS's and Sally's answers regarding the probability as your question seems to ask. However, may I add one small point? You said you weren't referring to the edge and yet your question mentioned "full odds of 3,4,5x." As you may have noticed in their calculations, the amount of odds taken/laid has absolutely nothing to do with the probability of winning or losing points. Dice don't know how much is being wagered, so the probability of any event is unaffected by the size of the wager.

The amount of odds taken/laid are indeed a factor when computing the combined edge. So I'm wondering if your question really meant to ask something else?

Quote: longtimelancer

My feeling is that the don't pass is more fun because you win more often (albeit with less money won).

Well, if winning more often after a point has been established, is more fun than losing more often on the come-out roll, then your EV of having fun will definitely be positive!

Steen

Quote: mustangsally

Yes, sure fun to win more often.
I get for the pass = 67/165 or 40.6061%
(1/12+2/15+25/132)
4&10: 2* 1/8 * 1/3 = 1/12
5&9: 2* 1/6 * 2/5 = 2/15
6&8: 2* 5/24 * 5/11 = 25/132

that makes the don't = 98/165 or 59.3939%

Find a friend that bets the don't pass and does not lay the full odds.
Make only the lay odds bet
should be no problem finding a nice win streak
0% house edge and win win win
Sally

Not sure if I understand. Does 40.6061% include the come-out roll or is it just the odds bet?

Quote: longtimelancer

Not sure if I understand. Does 40.6061% include the come-out roll or is it just the odds bet?

NO. You asked about the odds bet
"What is the probability of winning for both pass and don't pass with full odds without the point specified?"
one does not make the odds bet for the pass/don't pass on the come out roll

the probability of the pass/don't pass to win
for that from here:
https://wizardofodds.com/games/craps/appendix/1/
Pass/Come
The overall probability of winning is 8/36 + 9648/35640 = 17568/35640 = 244/495
and as a percentage = about 49.292929292929292929292929292929%
or about 49.3%

Don't Pass/Don't Come
The total probability of winning is 3/36 + 14112/35640 = 17082/35640 = 2847/5940
and as a percentage = about 47.93% or about 47.9%
But this figure includes all the pushes that can happen.

If one does not consider a push as a bet revolved (win/lose only) then
The overall probability of winning is 949/1925
and as a percentage = about 49.298701298701298701298701298701%
or about 49.3%

Sally